Consider a DF containing a single column having datetime values as shown:
df = pd.DataFrame(pd.date_range('1/1/2016', periods=10, freq='D'), columns=['Date'])

Concatenate a sample of the original DF with itself to create duplicated values(say, 5)
df_dups = pd.concat([df, df.sample(n=5, random_state=42)], ignore_index=True)
Compute it's unique counts by stacking it into a series object.
plotting_df = df_dups.stack().value_counts().reset_index(name='counts')
Scatter Plot:
As only numerical values are supported for both x and y axis as args for the built-in scatter plot method, we must call the plot_date function of matplotlib axes object to retain the dates as it is.
fig, ax = plt.subplots()
ax.plot_date(plotting_df['index'], plotting_df['counts'], fmt='.', color='k')
ax.set_ylim(0, plotting_df['counts'].values.max()+1)
fig.autofmt_xdate()
plt.xlabel('Date')
plt.ylabel('Counts')
plt.show()

I'm having trouble with the dates in the x axis part.?DataFrame. How would I do that if I have, for example, aDataFramewith just one column, the column called dates which has onedatetimevalue in each row?